High-Energy Expansion of Two-Loop Massive Four-Point Diagrams

Understand

We apply the method of regions to the massive two-loop integrals appearing in the Higgs pair production cross section at the next-to-leading order, in the high energy limit.

• For the non-planar integrals, a subtle problem arises because of the indefinite sign of the second Symanzik polynomial.
• We solve this problem by performing an analytic continuation of the Mandelstam variables such that the second Symanzik polynomial has a definite sign.
• Furthermore, we formulate the procedure of applying the method of regions systematically.